There are several genres, such as detective ficton, whete the main character is largely constant, but the puzzles (crimes to solve) change. After a while they become repetitive, but I have enjoyed quite a few mystery and adventure series (mostly written a few decades ago) with such an approach.
The Ellery Queen and Nero Wolf series were both very good in that way. Dad was a big Nero Wolf fan, so I was exposed to them fairly early on, too young to fully appreciate them, I think.
I also enjoyed the Mrs. Pollifax series by Dorothy Gilman; I saw the movie they made from the first book as a double bill with Snow White at a drive-in when very young, so when I stumbled across the first book after graduating from high school in a bookstore and determined upon reading the description that it was the basis for the movie I dimly remembered from my early childhood, I purchased it and read it; since then I've collected the entire series, haven't read them in years, but still have them.